Linear Operators: General theory |
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Page 46
... equal to the cardinality of B and if the cardinality of B is at most equal to the cardinality of A , then these two sets have the same cardinality . ) 3 If X is a vector space over Ø , 46 I.14.1 I. PRELIMINARY CONCEPTS Exercises ·
... equal to the cardinality of B and if the cardinality of B is at most equal to the cardinality of A , then these two sets have the same cardinality . ) 3 If X is a vector space over Ø , 46 I.14.1 I. PRELIMINARY CONCEPTS Exercises ·
Page 575
... equal to zero for μ in a neighborhood of σ , and equal to ( 2 — μ ) -1 for μ in a neighbor- hood of the remaining points of o ( T ) . Then g ( T ) ( λI —T ) = ( 21 — T ) g ( T ) = I - E ( o ) . If we define A1 : X → X by Д1x = X by Ax ...
... equal to zero for μ in a neighborhood of σ , and equal to ( 2 — μ ) -1 for μ in a neighbor- hood of the remaining points of o ( T ) . Then g ( T ) ( λI —T ) = ( 21 — T ) g ( T ) = I - E ( o ) . If we define A1 : X → X by Д1x = X by Ax ...
Page 716
... equal to one . Also the function identically equal to one is left fixed by T , so 1 € σ ( T ) . In the study of such processes one makes additional hypotheses on P which will guarantee that there exists an integer n and a compact ...
... equal to one . Also the function identically equal to one is left fixed by T , so 1 € σ ( T ) . In the study of such processes one makes additional hypotheses on P which will guarantee that there exists an integer n and a compact ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ